On the Kazhdan–Lusztig order on cells and families

  • Meinolf Geck

    Universität Stuttgart, Germany


We consider the set Irr(W) of (complex) irreducible characters of a finite Coxeter group W. The Kazhdan–Lusztig theory of cells gives rise to a partition of Irr(W) into “families” and to a natural partial order LR\leq_{\mathcal{LR}} on these families. Following an idea of Spaltenstein, we show that LR\leq_{\mathcal{LR}} can be characterised (and effectively computed) in terms of standard operations in the character ring of W. If, moreover, W is the Weyl group of an algebraic group G, then LR\leq_{\mathcal{LR}} can be interpreted, via the Springer correspondence, in terms of the closure relation among the “special” unipotent classes of G.

Cite this article

Meinolf Geck, On the Kazhdan–Lusztig order on cells and families. Comment. Math. Helv. 87 (2012), no. 4, pp. 905–927

DOI 10.4171/CMH/273